Problem: Solve for $x$ and $y$ using substitution. ${6x+5y = -2}$ ${y = -2x+2}$
Answer: Since $y$ has already been solved for, substitute $-2x+2$ for $y$ in the first equation. ${6x + 5}{(-2x+2)}{= -2}$ Simplify and solve for $x$ $6x-10x + 10 = -2$ $-4x+10 = -2$ $-4x+10{-10} = -2{-10}$ $-4x = -12$ $\dfrac{-4x}{{-4}} = \dfrac{-12}{{-4}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = -2x+2}\thinspace$ to find $y$ ${y = -2}{(3)}{ + 2}$ $y = -6 + 2$ $y = -4$ You can also plug ${x = 3}$ into $\thinspace {6x+5y = -2}\thinspace$ and get the same answer for $y$ : ${6}{(3)}{ + 5y = -2}$ ${y = -4}$